Second, each such experience is highly integrated. You cannot force yourself to see the world in black and white; its color is an integrated part of your view. Whatever information you are conscious of is wholly and completely presented to your mind; it cannot be subdivided. Underlying this unity of consciousness is a multitude of causal interactions among the relevant parts of your brain. If parts of the brain become fragmented and balkanized, as occurs in deep sleep or in anesthesia, consciousness fades.
To be conscious, then, you need to be a single, integrated entity with a large repertoire of highly differentiated states. Even if the hard disk on my laptop exceeds in capacity my lifetime memories, none of its information is integrated. The family photos on my Mac are not linked to one another. The computer does not know that the boy in those pictures is my son as he matures from a toddler to an awkward teenager and then a graceful adult. To my computer, all information is equally meaningless, just a vast, random tapestry of 0s and 1s. Yet I derive meaning from these images because my memories are heavily cross-linked. And the more interconnected, the more meaningful they become.
These ideas can be precisely expressed in the language of mathematics using notions from information theory such as entropy. Given a particular brain, with its neurons in a particular state—these neurons are firing while those ones are quiet—one can precisely compute the extent to which this network is integrated. From this calculation, the theory derives a single number, &PHgr; (pronounced “fi”) [see “A Theory of Consciousness,” Consciousness Redux; Scientific American Mind, July/August 2009]. Measured in bits, &PHgr; denotes the size of the conscious repertoire associated with the network of causally interacting parts being in one particular state. Think of &PHgr; as the synergy of the system. The more integrated the system is, the more synergy it has and the more conscious it is. If individual brain regions are too isolated from one another or are interconnected at random, &PHgr; will be low. If the organism has many neurons and is richly endowed with synaptic connections, &PHgr; will be high. Basically, &PHgr; captures the quantity of consciousness. The quality of any one experience—the way in which red feels different from blue and a color is perceived differently from a tone—is conveyed by the informational geometry associated with &PHgr;. The theory assigns to any one brain state a shape, a crystal, in a fantastically high-dimensional qualia space. This crystal is the system viewed from within. It is the voice in the head, the light inside the skull. It is everything you will ever know of the world. It is your only reality. It is the quiddity of experience. The dream of the lotus eater, the mindfulness of the meditating monk and the agony of the cancer patient all feel the way they do because of the shape of the distinct crystals in a space of a trillion dimensions—truly a beatific vision. The water of integrated information is turned into the wine of experience.
Integrated information makes very specific predictions about which brain circuits are involved in consciousness and which ones are peripheral players (even though they might contain many more neurons, their anatomical wiring differs). The theory has most recently been used to build a consciousness meter to assess, in a quantitative manner, the extent to which anesthetized subjects or severely brain-injured patients, such as Terri Schiavo, who died in Florida in 2005, are truly not conscious or do have some conscious experiences but are unable to signal their pain and discomfort to their loved ones [see “A Consciousness Meter,” Consciousness Redux; Scientific American Mind, March/April 2013].
IIT addresses the problem of aggregates by postulating that only “local maxima” of integrated information exist (over elements and spatial and temporal scales): my consciousness, your consciousness, but nothing in between. That is, every person living in the U.S. is, self by self, conscious, but there is no superordinate consciousness of the U.S. population as a whole.